The number of pairs lying between 40 and 100 such that HCF is 15, is L

Options

A. 3
B. 4
C. 5
D. 6

Answer

To find the number of pairs of numbers between 40 and 100 such that their Highest Common Factor (HCF) is 15, we can follow these steps:

### Step 1: Identify the multiples of 15 between 40 and 100
The first step is to find the multiples of 15 that lie within the range of 40 to 100. We can calculate this by finding the smallest multiple of 15 greater than or equal to 40 and the largest multiple of 15 less than or equal to 100.

- The smallest multiple of 15 greater than or equal to 40 is 45 (15 × 3).
- The largest multiple of 15 less than or equal to 100 is 90 (15 × 6).

The multiples of 15 in this range are:
- 45, 60, 75, 90.

### Step 2: List the identified multiples
Now, we list the identified multiples:
- 45
- 60
- 75
- 90

### Step 3: Form pairs from the identified multiples
Next, we need to form pairs from these numbers. The pairs should be unique combinations of the numbers listed above.

The possible pairs are:
1. (45, 60)
2. (45, 75)
3. (45, 90)
4. (60, 75)
5. (60, 90)
6. (75, 90)

### Step 4: Count the pairs
Now, we count the total number of unique pairs formed:
- Total pairs = 6

### Conclusion
Thus, the number of pairs lying between 40 and 100 such that their HCF is 15 is **6**.

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